Details

sample63.0ms

Algorithm

intervals

Results

42.0ms

267×

body

valid

simplify30.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

30.0ms

(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

prune33.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.7b

localize17.0ms

Local error

Found 2 expressions with local error:

22.7b	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
0.5b	(fma x.re y.re (* x.im y.im))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
4×	`add-cbrt-cube` `add-exp-log`
3×	`associate-/r` `associate-/l`
2×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `fma-udef` `div-inv`

Counts

2 → 41

Calls

2 calls:

Slowest

4.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
0.0ms	(fma x.re y.re (* x.im y.im))

series201.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

136.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
65.0ms	(fma x.re y.re (* x.im y.im))

simplify1.2s

Counts

31 → 47

Calls

31 calls:

Slowest

480.0ms	(/ (* (* (fma x.re y.re (* x.im y.im)) (fma x.re y.re (* x.im y.im))) (fma x.re y.re (* x.im y.im))) (* (* (fma y.im y.im (* y.re y.re)) (fma y.im y.im (* y.re y.re))) (fma y.im y.im (* y.re y.re))))
90.0ms	(/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (* (cbrt (fma y.im y.im (* y.re y.re))) (cbrt (fma y.im y.im (* y.re y.re)))))
51.0ms	(/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (sqrt (fma y.im y.im (* y.re y.re))))
47.0ms	(/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) 1)
46.0ms	(/ (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma y.im y.im (* y.re y.re))))

prune634.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 22.3b

localize44.0ms

Local error

Found 4 expressions with local error:

29.2b	(sqrt (fma y.im y.im (* y.re y.re)))
29.2b	(sqrt (fma y.im y.im (* y.re y.re)))
14.2b	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
0.5b	(fma x.re y.re (* x.im y.im))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 87

Calls

4 calls:

Slowest

10.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
3.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
2.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
1.0ms	(fma x.re y.re (* x.im y.im))

series359.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

151.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
80.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
69.0ms	(fma x.re y.re (* x.im y.im))
59.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.8s

Counts

68 → 99

Calls

68 calls:

Slowest

335.0ms	(/ (* (* (fma x.re y.re (* x.im y.im)) (fma x.re y.re (* x.im y.im))) (fma x.re y.re (* x.im y.im))) (* (* (sqrt (fma y.im y.im (* y.re y.re))) (sqrt (fma y.im y.im (* y.re y.re)))) (sqrt (fma y.im y.im (* y.re y.re)))))
83.0ms	(/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (* (cbrt (sqrt (fma y.im y.im (* y.re y.re)))) (cbrt (sqrt (fma y.im y.im (* y.re y.re))))))
45.0ms	(/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (sqrt 1))
44.0ms	(/ (sqrt (fma x.re y.re (* x.im y.im))) (sqrt (* (cbrt (fma y.im y.im (* y.re y.re))) (cbrt (fma y.im y.im (* y.re y.re))))))
43.0ms	(/ 1 (* (cbrt (sqrt (fma y.im y.im (* y.re y.re)))) (cbrt (sqrt (fma y.im y.im (* y.re y.re))))))

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 18.8b

localize34.0ms

Local error

Found 2 expressions with local error:

22.7b	(/ (fma y.im x.im (* y.re x.re)) (fma y.im y.im (* y.re y.re)))
0.3b	(fma y.im x.im (* y.re x.re))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
4×	`add-cbrt-cube` `add-exp-log`
3×	`associate-/r` `associate-/l`
2×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `fma-udef` `div-inv`

Counts

2 → 41

Calls

2 calls:

Slowest

8.0ms	(/ (fma y.im x.im (* y.re x.re)) (fma y.im y.im (* y.re y.re)))
0.0ms	(fma y.im x.im (* y.re x.re))

series171.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

126.0ms	(/ (fma y.im x.im (* y.re x.re)) (fma y.im y.im (* y.re y.re)))
45.0ms	(fma y.im x.im (* y.re x.re))

simplify1.1s

Counts

31 → 47

Calls

31 calls:

Slowest

398.0ms	(/ (* (* (fma y.im x.im (* y.re x.re)) (fma y.im x.im (* y.re x.re))) (fma y.im x.im (* y.re x.re))) (* (* (fma y.im y.im (* y.re y.re)) (fma y.im y.im (* y.re y.re))) (fma y.im y.im (* y.re y.re))))
49.0ms	(/ (* (cbrt (fma y.im x.im (* y.re x.re))) (cbrt (fma y.im x.im (* y.re x.re)))) (* (cbrt (fma y.im y.im (* y.re y.re))) (cbrt (fma y.im y.im (* y.re y.re)))))
42.0ms	(/ (fma y.im x.im (* y.re x.re)) (sqrt (fma y.im y.im (* y.re y.re))))
39.0ms	(/ (fma y.im x.im (* y.re x.re)) (cbrt (fma y.im y.im (* y.re y.re))))
36.0ms	(/ (sqrt (fma y.im x.im (* y.re x.re))) (cbrt (fma y.im y.im (* y.re y.re))))

prune600.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 18.8b

localize48.0ms

Local error

Found 4 expressions with local error:

29.2b	(sqrt (fma y.im y.im (* y.re y.re)))
29.2b	(sqrt (fma y.im y.im (* y.re y.re)))
14.2b	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
0.5b	(fma x.re y.re (* x.im y.im))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 87

Calls

4 calls:

Slowest

10.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
2.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
2.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
0.0ms	(fma x.re y.re (* x.im y.im))

series337.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

152.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
71.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
70.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
43.0ms	(fma x.re y.re (* x.im y.im))

simplify1.9s

Counts

68 → 99

Calls

68 calls:

Slowest

256.0ms	(/ (* (* (fma x.re y.re (* x.im y.im)) (fma x.re y.re (* x.im y.im))) (fma x.re y.re (* x.im y.im))) (* (* (sqrt (fma y.im y.im (* y.re y.re))) (sqrt (fma y.im y.im (* y.re y.re)))) (sqrt (fma y.im y.im (* y.re y.re)))))
86.0ms	(/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (* (cbrt (sqrt (fma y.im y.im (* y.re y.re)))) (cbrt (sqrt (fma y.im y.im (* y.re y.re))))))
54.0ms	(/ (sqrt (fma x.re y.re (* x.im y.im))) (* (cbrt (sqrt (fma y.im y.im (* y.re y.re)))) (cbrt (sqrt (fma y.im y.im (* y.re y.re))))))
51.0ms	(/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (sqrt (sqrt (fma y.im y.im (* y.re y.re)))))
49.0ms	(- (log (fma x.re y.re (* x.im y.im))) (log (sqrt (fma y.im y.im (* y.re y.re)))))

prune1.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 18.8b

regimes324.0ms

Accuracy

4% (2.7b remaining)

Error of 25.6b against oracle of 22.8b and baseline of 25.7b

bsearch58.0ms

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.2s

8464×

body

valid